Re: 4 cores or 6
I would go with the cheaper option to be honest. (I guess thats the 4 core) Your requirements from your system arent very intensive compared to others. Plus the Phenom X 4 is a nice processor anyway. (If you did get the black edition of the processor you could overclock it to get a little more power out of it if needed - although I doubt you would need it)
There would obviously be a gain as in the difference between the 2, but you wont see it with the tasks you are doing to be honest.
R.E. The intel bit, as above, I would stay with the cheap option (Which would probably work out to AMD over Intel) Intel wise, you could go for the i3 processor, for a cheap solution, that should just about fill all requirements. Alternatively the i5 processor, or the sandybridge i5 2500k processor, will both handle those tasks with relative ease. If you did want to spend the extra and get an i7 processor you would get more power - but again, its a waste as you really dont need it.
Either processor (AMD Phenom x 4, or the i5 range) should see you fine for a good few years, but if it was me I would be plumping for the quad core all day. It just depends on the money you want to put in it.